Alexander and writhe polynomials for virtual knots

Blake Mellor

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arXiv · 1601.07153

Alexander and writhe polynomials for virtual knots

Blake Mellor

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Abstract

We give a new interpretation of the Alexander polynomial $\Delta_0$ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, $\Delta_0$ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

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Blake Mellor. 2016-01-26. Alexander and writhe polynomials for virtual knots. https://arxiv.org/abs/1601.07153

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